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Quantum Teleportation Perspectives on Quantum Information Science Joe Lykken Fermilab ASCAC Meeting April 17, 2018 The age of quantum computing and quantum communications is getting closer Even after allowing for media hype, very impressive progress in the last few years on building real quantum computers and performing long- range quantum communication 2 4/17/18 Lykken | Perspectives on QIS | ASCAC What is a quantum digital computer? • Information is stored and manipulated as quantum states “qubits” • A single qubit state is in general a quantum superposition of two distinct states, which we will denote as state |0> and state |1>: • The two angles parameterize the surface of a sphere, called the Bloch sphere • Classical computing only accesses the North and South poles of the Bloch sphere 3 4/17/18 Lykken | Perspectives on QIS | ASCAC Quantum circuits • Given some number of qubits in arbitrary states, I can measure each qubit state • The measurement projects the n-qubit quantum state to an n-bit classical binary number • We call this a projection to the “computational basis” • This is the simplest quantum circuit • More generally we can perform a variety of unitary operations, called gates, on the qubits before making measurements • Gates operations can act on a single qubit, or on multiple qubits • Starting from a rather small menu of gates one can obtain a universal quantum computer 4 4/17/18 Lykken | Perspectives on QIS | ASCAC Can quantum circuits solve hard problems? • Here is a quantum circuit that maps a 3-qubit input state |x1>|x2>|x3> to an output state |y1>|y2>|y3>, where • This is a (discrete) Fourier transform • The quantum circuit uses two kinds of gate operations: • A Hadamard gate that acts on a single qubit: • A controlled phase shift: a two qubit gate that applies a phase shift to the target qubit that depends on the state of the control qubit 5 4/17/18 Lykken | Perspectives on QIS | ASCAC Exponential speedup • The discrete Fourier transform is an example of a calculation that a quantum computer can do exponentially faster than any classical computer: for n qubits we need ~ n2 gate operations, whereas a conventional Fast Fourier Transform requires ~ n2n operations • In 1994 Peter Shor showed that factorization of prime numbers can be done with a combination of quantum Fourier transforms and classical operations that run in polynomial time • Thus a quantum computer with a sufficiently large number of qubits and reliable single and 2-qubit gate operations can do at least one important calculation exponentially faster than a classical computer 6 4/17/18 Lykken | Perspectives on QIS | ASCAC Rapid progress in building quantum computers Moore’s Law is over (?) and has been replaced by Martinis’ Law (?): the number of qubits in high performance quantum computers will double every 18 months Google 22-qubit quantum computer, 2017 Google 72-qubit quantum computer, 2018 A performant 72-qubit quantum computer can achieve “quantum supremacy” = the ability to do at least some (not necessarily useful) calculations that cannot be reproduced by the world’s largest classical supercomputers 7 4/17/18 Lykken | Perspectives on QIS | ASCAC Analog computers • Analog computers are in principle more powerful for certain applications than universal digital computers • Classical analog computers were the dominant form of computing until fairly Antikythera mechanism, recently Greece circa 100 BCE Soap bubble Tide calculator USA until 1965 8 4/17/18 Lykken | Perspectives on QIS | ASCAC Richard Feynman 1981 “Nature isn’t classical, dammit, and if you want a simulation of nature, you’d better make it quantum mechanical” • First person to propose the idea of quantum computing and explain it’s potential importance • In addition to universal digital quantum computers, proposed quantum analog computers where the quantum behavior of the one system simulates the quantum behavior of some other system that you want to better understand • In other words, use quantum hardware to simulate quantum problems • This is very different from building a gate-based quantum computer to do prime factorization, which is a classical problem 9 4/17/18 Lykken | Perspectives on QIS | ASCAC Challenges of building quantum computers Need a qubit, i.e. a two-state quantum system, that you can manipulate and not confuse with other possible states of the system. You must be able to create states that are superpositions of your two basis states, and maintain the quantum coherence long enough to perform a series of quantum manipulations Examples of qubits: • Photon polarization • Photons in two time bins • Electron spin, nuclear spin, atomic spin • Ground state and particular excited state of an ion • Ground state and first excited state of a nonlinear oscillator, e.g. a superconducting Josephson Junction LC circuit 10 4/17/18 Lykken | Perspectives on QIS | ASCAC From qubits to quantum systems For good qubits you need • Quantum coherence • Pairwise coupling of qubits (for 2-qubit gates) • Ability to create initial state, perform qubit gate operations, and measure final state • Low rate of errors; ability to detect errors and do error correction Then scale this all up to a large quantum system Extra challenge: you cannot copy quantum information (no-cloning theorem) 11 4/17/18 Lykken | Perspectives on QIS | ASCAC Superconducting quantum computers Lots of groups working with variations on superconducting Josephson Junction circuits, in some cases with very fast and very high fidelity (low error rate) gate operations Similar performance with 2-qubit gates: 99.4%, 40 ns John Martinis superconducting Xmon qubits 12 4/17/18 Lykken | Perspectives on QIS | ASCAC Superconducting 3D quantum computers In 2011 the Yale group showed that there are great advantages to putting your Josephson Junction qubits inside superconducting microwave cavities Good for: • Isolation • Control • Readout Achieved record long quantum coherence times, as measured by T2, the dephasing time of H. Paik et al, PRL 107, 240501 (2011) superposition states 13 4/17/18 Lykken | Perspectives on QIS | ASCAC 3D qubits/cavities give the best quantum coherence T2 of ~ a millisecond means you can think about quantum circuits with depth ~ 10,000 Can we do even better? 14 Lykken | Perspectives on QIS | ASCAC 4/17/18 The science of superconducting cavities At Fermilab we use superconducting cavities in the microwave/RF frequency band for particle accelerators 15 4/17/18 Lykken | Perspectives on QIS | ASCAC The science of superconducting cavities At Fermilab we make SRF cavities from niobium, and assemble them into cryomodules that in turn are assembled into linear accelerators Alex Romanenko and Anna Grassellino lead the Fermilab SRF cavity program Cryomodule built at Fermilab for the new LCLS-II free electron laser light source at SLAC 16 4/17/18 Lykken | Perspectives on QIS | ASCAC The Q of superconducting cavities For an accelerator you want to achieve very high accelerating gradients (e.g. 30 megavolts/meter), and very high quality factor Q High Q means that the resonant cavities “ring” longer and thus need less microwave power pumped into them Thanks to recent breakthroughs by Fermilab scientists, we now routinely achieve Q near or above 1011 If Galileo had rung a bell with this value of Q, it would still be ringing today 17 4/17/18 Lykken | Perspectives on QIS | ASCAC Niobium SRF cavities for quantum computers? Challenges: • For accelerator cavities you want high gradients = as many photons as possible; for a quantum computer you want cavities containing a single microwave photon • Accelerators operate at temperatures around 2K, quantum computers around 20 milliKelvin 18 4/17/18 Lykken | Perspectives on QIS | ASCAC First try at T ~ 12 mK, down to ~1000 photons Q ~ 2 x 109 100 times better than previous record E ~ 1000 photons Publication with full details in preparation 19 4/17/18 Lykken | Perspectives on QIS | ASCAC Why does Fermilab care about superconducting qubits? Fermilab is devoted to basic research in high energy physics (HEP) 20 4/17/18 Lykken | Perspectives on QIS | ASCAC HEP experiments use a lot of computing 21 Lykken | Perspectives on QIS | ASCAC 4/17/18 HEP applications of quantum computers Long view: • Most particle physics applications will require thousands, if not millions, of error-corrected qubits, which won’t be available for ~20 years • However Fermilab is planning experiments that will be running 20 years from now, e.g. the DUNE neutrino experiment, and the CMS experiment at the LHC What can we do now? • Identify pieces of problems that we care about that can be addressed with near-term quantum technologies 22 4/17/18 Lykken | Perspectives on QIS | ASCAC Applications of today’s quantum computers: quantum machine learning • Many particle physics experiments already using deep learning to better classify, e.g. neutrino-induced interactions in particle detectors • Some standard machine learning techniques, e.g. Boltzmann machines, involve estimating the ground state of a Hamiltonian that has many local minima 23 4/17/18 Lykken | Perspectives on QIS | ASCAC Applications of today’s quantum computers: quantum machine learning with quantum annealers • Annealing is a standard classical process for trying to avoid getting stuck in a local minimum • Quantum annealing improves this by adding the possibility of quantum tunneling • D-Wave makes a quantum computer with 2,000 superconducting qubits that functions as a quantum annealer • This is an analog quantum computer, not a gate-programmable computer 24 4/17/18 Lykken
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